The semiclassical limit of the coherent state propagator involves complex classical trajectories of the Hamiltonian H(u,v) = satisfying u(0) = z' and v(T) = z"*. In this work we study mostly the case z' = z". The propagator is then the return probability amplitude of a wave packet. We show that a plot of the exact return probability brings out the quantal images of the classical periodic orbits. Then we compare the exact return probability with its semiclassical approximation for a soft chaotic system with two degrees of freedom. We find two situations where classical trajectories satisfying the correct boundary conditions must be excluded from the semiclassical formula. The first occurs when the contribution of the trajectory to the propagator becomes exponentially large as Planck's over 2 pi goes to zero. The second occurs when the contributing trajectories undergo bifurcations. Close to the bifurcation the semiclassical formula diverges. More interestingly, in the example studied, after the bifurcation, where more than one trajectory satisfying the boundary conditions exist, only one of them in fact contributes to the semiclassical formula, a phenomenon closely related to Stokes lines. When the contributions of these trajectories are filtered out, the semiclassical results show excellent agreement with the exact calculations.

We consider a semiclassical approximation, first derived by Heller and coworkers, for the time evolution of an originally gaussian wave packet in terms of complex trajectories.We also derive additional approximations replacing the complex trajectories by real ones. These yield three different semiclassical formulae involving different real trajectories. One of these formulae is Heller's thawed gaussian approximation. The other approximations are non-gaussian and may involve several trajectories determined by mixed initial-final conditions. These different formulae are tested for the cases of scattering by a hard wall, scattering by an attractive gaussian potential, and bound motion in a quartic oscillator. The formula with complex trajectories gives good results in all cases. The non-gaussian approximations with real trajectories work well in some cases, whereas the thawed gaussian works only in very simple situations.

Recently, Bohr's complementarity principle was assessed in setups involving delayed choices. These works argued in favor of a reformulation of the aforementioned principle so as to account for situations in which a quantum system would simultaneously behave as wave and particle. Here we defend a framework that, supported by well-known experimental results and consistent with the decoherence paradigm, allows us to interpret complementarity in terms of correlations between the system and an informer. Our proposal offers formal definition and operational interpretation for the dual behavior in terms of both nonlocal resources and the couple work-information. Most importantly, our results provide a generalized information-based tradeoff for the wave-particle duality and a causal interpretation for delayed-choice experiments.

The notion of integrability is discussed for classical nonautonomous systems with one degree of freedom. The analysis is focused on models which are linearly spanned by finite Lie algebras. By constructing the autonomous extension of the time-dependent Hamiltonian we prove the existence of two invariants in involution which are shown to obey the criterion of functional independence. The implication of this result is that chaotic motion cannot exist in these systems. In addition, if the invariant manifold is compact, then the system is Liouville integrable. As an application, we discuss regimes of integrability in models of dynamical tunneling and parametric resonance, and in the dynamics of two-level systems under generic classical fields. A corresponding quantum algebraic structure is shown to exist which satisfies analog conditions of Liouville integrability and reproduces the classical dynamics in an appropriate limit within the Weyl-Wigner formalism. The quantum analog is then conjectured to be integrable as well.

We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin-orbit interactions and the Jaynes-Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit.As special cases we consider separable systems, the limit of very large spins and the case of spin 1/2.